Abstract

Photonic crystal fibers made from arbitrary base materials are considered, and a unified semianalytical approach for the dispersion and modal properties is derived that applies to the short-wavelength regime. In particular, the dispersion and the effective index are calculated and compared with fully vectorial plane-wave simulations, and excellent agreement is found. Asymptotic results for the mode-field diameter and the V parameter are also calculated, and from the latter it is predicted that the fibers are endlessly single mode for a normalized airhole diameter smaller than 0.42, independently of the base material.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]

2004 (1)

2003 (4)

2001 (1)

1997 (1)

1996 (1)

Atkin, D. M.

Bird, D. M.

Birks, T. A.

Bjarklev, A.

Folkenberg, J. R.

Hansen, K. P.

Hedley, T. D.

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Johnson, S. G.

Knight, J. C.

Lægsgaard, J.

J. Riishede, N. A. Mortensen, and J. Lægsgaard, J. Opt. A Pure Appl. Opt. 5, 534 (2003).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Mortensen, N. A.

Nielsen, M. D.

Pottage, J. M.

Riishede, J.

J. Riishede, N. A. Mortensen, and J. Lægsgaard, J. Opt. A Pure Appl. Opt. 5, 534 (2003).
[CrossRef]

Russell, P. St. J.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (3)

Fig. 1
Fig. 1

(A) Geometrical eigenvalues γ 2 for the fundamental core ( c , 1 ) , the second-order core ( c , 2 ) and the fundamental cladding (cl) modes versus normalized airhole diameter d Λ . (B) Corresponding V parameter. (C) Effective mode-field radius of the fundamental core mode. The data points are obtained from finite-element simulations[7] of Eq. (4), and the dashed curves are guides to the eyes. The gray region indicates the endlessly single-mode regime with V PCF < π .

Fig. 2
Fig. 2

Effective index n eff of the fundamental core mode versus normalized wavelength λ Λ for holey fibers with normalized airhole diameter d Λ = 0.4 and varying base material. The dashed curves are the predictions of Eq. (8), and the data points are the results of fully vectorial plane-wave simulations.[11] Inset, fiber geometry and the fundamental core eigenfunction ψ c with γ c 2 = 7.0506 , obtained with a finite-element simulation.[7]

Fig. 3
Fig. 3

Effective index n eff of the fundamental cladding mode versus normalized wavelength λ Λ for holey fibers with normalized airhole diameter d Λ = 0.4 and varying base material. The dashed curves are the predictions of Eq. (8), and the data points are results of fully vectorial plane-wave simulations.[11] Inset, unit cell of the periodic cladding structure and the fundamental cladding eigenfunction ψ cl with γ cl 2 = 15.5728 , obtained with the aid of a finite-element simulation.[7]

Equations (8)

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× × E ( r ) = ϵ ( r ) ω 2 c 2 E ( r ) .
2 E ( r ) = ϵ b ω 2 c 2 E ( r ) ,
ω = ( Ω x y 2 + Ω z 2 ) 1 2 = c n b ( γ 2 Λ 2 + β 2 ) 1 2 ,
Λ 2 ( x 2 + y 2 ) ψ ( x , y ) = γ 2 ψ ( x , y ) ,
γ c 2 A + B d Λ + C ( d Λ ) 2 + D ( d Λ ) 3 ,
lim λ Λ V PCF = ( γ cl 2 γ c 2 ) 1 2 ,
lim λ Λ A eff = d x d y ψ ( x , y ) 2 d x d y ψ ( x , y ) 2 d x d y ψ ( x , y ) 4 .
n eff = n b [ 1 γ 2 4 π 2 n b 2 ( λ Λ ) 2 ] 1 2 ,

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